2026/4/27-2026/5/1, Ludovic Goudenege (Université d'Evry-Paris Saclay)
会場：早稲田大学
タイトル：Numerical Schemes for SDEs and PDEs with Applications to Quantitative Finance
アブストラクト： This course introduces numerical methods for stochastic differential equations (SDEs) and partial differential equations (PDEs), with applications to quantitative finance. It presents the fundamental link between sampling stochastic models and pricing PDEs through the Feynman–Kac formula.
The course covers time discretization schemes for SDEs, tree-based and Monte Carlo methods, as well as finite difference and related methods for PDEs. Applications include European and American option pricing, high-dimensional models, and optimal stopping problems.
Finally, modern machine learning techniques are introduced as efficient tools for pricing in high dimensions, particularly when classical numerical methods become impractical. Hybrid approaches combining Monte Carlo simulation, exact integration, and learning-based methods are discussed in both Markovian and non-Markovian settings.
講義形態(対面・オンライン)について変更される可能性があるため，参加予定の方は福泉先生 (fukuizumiATwaseda.jp)に事前にご連絡ください．(ATはアットマーク)
会場は以下の通りです．いずれも，西早稲田キャンパス51号館の部屋となります．
月(04/27) 17-06(2,4限) 17-04(3限)
火(04/28) 17-06(2,3,4限)
水(04/29) 18-06(2,3,4限)
木(04/30) 17-06(2,3,4限)
金(05/01) 17-08(2,3,4限)
早稲田の授業時間は以下の通りです．
2限 10:40～12:20
3限 13:10～14:50
4限 15:05～16:45